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Why lead chloride is soluble in hot water but not in cold water?
In general, most solutes SHOULD be more soluble in hot water. Why?
Let's look at the dissolution reaction:
##PbCl_2(s) rightleftharpoons Pb^(2+)(aq) + 2Cl^(-)(aq)##
Strong ionic bonds are broken in the reaction, i.e. the electrostatic bonds that bind the lead chloride lattice together. Of course, the water molecules solvate these ions, but the reaction still involves the breaking of strong chemical bonds. At higher temperatures, more bonds can be broken and the reaction proceeds to the right.
As chemists, as physical scientists, we should look at the data. This site gives a marginal increase in solubility as the temperature is raised.